When light–matter interaction leaves the perturbative regime, the system enters the strong-field or nonperturbative regime, where the response is no longer a simple sum of low-order nonlinear processes (like second-harmonic or third-harmonic generation). Instead, new physics emerges, especially in 2D materials, topological insulators, and strongly correlated systems. Here’s a detailed breakdown:

✅ 1. Perturbative vs. Nonperturbative Regime

• P=χ(1)E+χ(2)E2+χ(3)E3+…P = \chi^{(1)} E + \chi^{(2)} E^2 + \chi^{(3)} E^3 + \dotsP=χ(1)E+χ(2)E2+χ(3)E3+…Perturbative regime: Optical response can be described by a power series in the electric field EEE:
• Nonperturbative regime: Field strength is so large that: Higher-order terms cannot be truncated. Electrons can be driven across the band structure, causing effects beyond standard nonlinear optics. Dynamics are dominated by strong coupling rather than small perturbations.

✅ 2. What Happens in Strong Fields?

a) Band Structure Dynamics

• Electrons can traverse large portions of the Brillouin zone in a single optical cycle.
• Leads to: Bloch oscillations Wannier–Stark localization Dynamic band flattening (field-dressed bands) Floquet-Bloch states (periodically driven systems with new topological phases)

b) High Harmonic Generation (HHG)

• Strong fields cause coherent acceleration of electrons, then recombination, emitting high harmonics of the driving frequency.
• In 2D materials (graphene, TMDs): HHG becomes valley-selective → valleytronics HHG spectra carry band structure and Berry curvature information
• In topological insulators: HHG encodes topological invariants (e.g., Chern numbers)

c) Interband & Intraband Nonlinear Currents

• Electrons experience: Interband transitions (Zener tunneling across the gap) Intraband acceleration (nonlinear currents from Berry curvature)
• Leads to: Shift currents (bulk photovoltaic effect) Anomalous Hall currents driven by Berry curvature

d) Light-Induced Topological Phase Transitions

• Intense pulses can reshape the topology of bands: Close/reopen band gaps → induce Floquet topological phases Generate light-induced Chern insulators
• This means topology becomes dynamically controllable by light.

e) Breakdown of Adiabatic Approximation

• Electron motion no longer adiabatic → Landau–Zener tunneling becomes significant.
• Strong fields can ionize bound states (like excitons) or even create electron–hole plasmas.

f) Extreme Nonlinear Optical Phenomena

• Carrier-envelope phase effects: Single-cycle fields control electron trajectories.
• Attosecond electron dynamics in solids → opens route to petahertz electronics.
• Nonperturbative multiphoton absorption: Cannot be described by simple nnn-photon absorption.

✅ 3. Why 2D and Topological Materials are Special

• Reduced dimensionality → stronger light–matter coupling.
• Berry curvature and topology → strong effects on nonlinear currents (shift, injection).
• Edge states in topological insulators: Nonlinear driving can create edge solitons. Possible topology inversion under strong fields.
• Graphene: Gapless structure allows high harmonic generation up to very high orders.

✅ 4. Applications & Frontiers

• Ultrafast control of topological phases for electronics.
• Valley-selective currents in TMDs → quantum information.
• HHG spectroscopy to probe correlated materials.
• Floquet engineering of quantum materials.
• Strong-field QED analogs in condensed matter (Schwinger effect analog).

Summary in One Line:

When you leave the perturbative regime, light does not just “probe” the material; it reshapes the material’s electronic structure, creates new topological states, and induces nonlinear quantum phenomena like HHG, Floquet phases, and strong-field tunneling.

When light–matter interaction leaves the perturbative regime (under very intense pulses), the material response becomes strongly nonlinear and cannot be described by a few susceptibilities like χ(2)\chi^{(2)}χ(2) or χ(3)\chi^{(3)}χ(3).

What happens?

Examples:

• Graphene: High-intensity pulses generate harmonics up to the 9th order or more.
• Topological insulators (e.g., Bi2_22​Se3_33​): Intense light can induce photocurrents via Berry curvature without external bias.